## Preprints (rote Reihe) des Fachbereich Mathematik

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#### Year of publication

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#### Keywords

- Hochschild homology (1)
- Hochschild-Homologie (1)
- Homologietheorie (1)
- Quasi-identities (1)
- Stratifaltigkeiten (1)
- Zyklische Homologie (1)
- cyclic homology (1)
- hyper-quasi-identities (1)
- hyperquasivarieties (1)
- non-commutative geometry (1)

336

Hyperquasivarieties
(2003)

334

We define a class of topological spaces (LCNT-spaces) which come together with a nuclear Frechet algebra. Like the algebra of smooth functions on a manifold, this algebra carries the differential structure of the object. We compute the Hochschild homology of this object and show that it is isomorphic to the space of differential forms. This is a generalization of a result obtained by Alain Connes in the framework of smooth manifolds.

332

In recent years a considerable attention was paid to an investigation of finite orders relative to different properties of their isotone functions [2,3]. Strict order relations are defined as strict asymmetric and transitive binary relations. Some algebraic properties of strict orders were already studied in [6]. For the class K of so-called 2-series strict orders we describe the partially ordered set EndK of endomorphism monoids, ordered by inclusion. It is obtained that EndK possesses a least element and in most cases defines a Boolean algebra. Moreover, every 2-series strict order is determined by its n-ary isotone functions for some natural number n.